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Chapter 12
Cascade, Ratio, and
Feedforward Control
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Overall Course Objectives Develop the skills necessary to function as
an industrial process control engineer. Skills
Tuning loops
Control loop design Control loop troubleshooting
Command of the terminology
Fundamental understanding Process dynamics
Feedback control
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Cascade, Ratio, and FeedforwardControl
Each of these techniques offers advantageswith respect to disturbance rejection:
Cascade reduces the effect of specific types of
disturbances.
Ratio reduces the effect of feed flow rates
changes
Feedforward control is a general methodology
for compensating for measured disturbances.
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Compensating for Disturbances
Reduces Deviations from
Setpoint and Settling Time
-6
-3
0
3
6
0 10 20 30 40 50
Time (seconds)
T'(K)
FB-only
Compensating
for disturbances
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Level Controller on a Tank With
and Without Cascade Control
Fin
FC
LT
RSP
FT
Fout
Lsp
LC
Fin
LT
Fout
Lsp
LC
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Analysis of Cascade Example
Without a cascade level controller, changes
in downstream pressure will disturb the tank
level.
With cascade level controller, changes indownstream pressure will be absorbed by the
flow controller before they can significantly
affect tank level because the flow controllerresponds faster to this disturbance than the
tank level process.
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Key Features for CascadeControl to be Successful
Secondary loop should reduce the effect of
one or more disturbances.
Secondary loop must be at least 3 times faster
than master loop.
The CV for the secondary loop should have adirect effect on the CV for the primary loop.
The secondary loop should be tuned tightly.
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Cascade Reactor Temperature
Control
Feed
ProductTT
Cooling
water
TC
Feed
Product
TT
Cooling
water
TCTT
TC
RSP
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Analysis of Example
Without cascade, changes in the coolingwater temperature will create a significant
upset for the reactor temperature.
With cascade, changes in the cooling water
temperature will be absorbed by the slave
loop before they can significantly affect thereactor temperature.
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Multiple Cascade Example
This approach works because the flow control
loop is much faster than the temperature control
loop which is much faster than the composition
control loop.
FT
AC
AT
TCTT
FC
RSP
RSP
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Example
TT
PT
Condensate
Steam
Feed
Draw schematic: A temperature controller on theoutlet stream is cascaded to a pressure controller
on the steam which is cascaded to a control valve
on the condensate.
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Solution
TT
PTPCTC
Condensate
Steam
RSP
Feed
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Ratio Control
Useful when the manipulated variable scalesdirectly with the feed rate to the process.
Dynamic compensation is required when the
controlled variable responds dynamically
different to feed rate changes than it does to
a changes in the manipulated variable.
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Typical Performance
Improvements using Ratio Control
Time
ImpurityConcentration
w/ ratio control
w/o ratio control
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Ratio Control for Wastewater
Neutralization
NaOH
SolutionAcid
Wastewater
Effluent
FTFT
FC
pHTpHC
RSP
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Analysis of Ratio ControlExample
The flow rate of base scales directly withthe flow rate of the acidic wastewater.
The output of the pH controller is the ratio
of NaOH flow rate to acid wastewater flow
rate; therefore, the product of the controller
output and the measured acid wastewater
flow rate become the setpoint for the flow
controller on the NaOH addition.
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Ratio Control Applied for VentComposition Control
Steam
Feed
Product
TT
FT
FCFT AT
AC
Vent
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Ratio Control Requiring
Dynamic Compensation
FT
AC
AT
FC
RSP
FT
Feed
DC
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Example
FT
FT TT
FlueGas
Process
FluidFuel
Draw schematic: For a control system that adjuststhe ratio of fuel flow to the flow rate of the process
fluid to control the outlet temperature of the process
fluid. Use a flow controller on the fuel.
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Solution
FT
FC
FT TT
TC
RSP FlueGas
Process
FluidFuel
Ratio
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Feedforward and Feedback Level
Control
Make-up
Water
To Steam
Users
LT
LC
Make-up
Water
To Steam Users
LT
FT
FF
To Steam
Users
LT
FT FF
LC +
Make-up Water
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Analysis of Feedforward and
Feedback Level Control
Feedback-only must absorb the variations insteam usage by feedback action only.
Feedforward-only handle variation in steam
usage but small errors in metering will
eventually empty or fill the tank.
Combined feedforward and feedback hasbest features of both controllers.
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Derivation of FF Controller
Cff(s)
Y(s)
Gd(s)
D(s)
+
+Ga(s)
Gff(s)
Gp(s)
Gds
(s)
)()()(
)()(
)(forSolving
0)()()()()()()()(
sGsGsG
sGsG
sG
sGsDsGsGsGsGsDsY
pads
dff
ff
dpaffds
=
=+=
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Lead/Lag Element for
Implementing FF Control
ffldff
s
ldff
s
dp
s
pd
ff
d
s
dd
p
s
ppads
K
s
esK
esK
esK
sG
s
eKsG
seKsGsGsG
ff
p
d
d
p
,,,:parametersLead/Lag
)1(
)1(
)1(
)1(
)(
1)(
1)()()(
lg
lg +
+
=+
+
=
+=
+=
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Effect of Lead/Lag Ratio
Time
cff
ld/ lg =
ld/ lg =1
ld/ lg = 2
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Static Feedforward Controller
ffff KsG =)(
A static feedforward controller make a correctionthat is directly proportional to the disturbancechange.
A static feedforward controller is used when theprocess responds in a similar fashion to a changein the disturbance and the manipulated variable.
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Feedforward When p
d
FF
FeedFT
Coolant
Outlet
Coolant
Inlet
TT
FT
FC
1)(
ld
s
+
=
s
eKsG
ff
ff
ff
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Example of Feedforward Control
for d
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Static Feedforward Results
-4
0
4
8
12
0 2 4 6 8 10Time
T'(C)
6.5 C
When the inlet temperature drops by 20C, Q isimmediately increased by 20 kW.
Deviations from setpoint result from dynamic
mismatch
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Perfect Feedforward Control
-30
-15
0
15
30
0 2 4 6 8 10Time (minutes)
T'(C)
Ti effect
Net result
FF Effect
FF correction is mirror image of disturbance effect.
Net effect is no change in controlled variable.
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Required Dynamic Compensation
0
10
20
0 2 4 6 8 10Time (minutes)
T(C)
Q=20kW
Perfect FF
Since the Q affects the process slower than Ti ,
initially overcompensation in Q is required
followed by cutting back on Q to 20 kW.
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Results with Dynamic
Compensation
-4
0
4
8
12
0 2 4 6 8 10
Time (minutes)
T'(C)
w/o DC
w/ DC
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Feedforward Control Action
0 5 10 15 20
Time (minutes)
Q
w/o DC
w/ DC
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Effect of Lead/Lag Ratio
Time
cff
ld/
lg =
ld/ lg = 1
ld/ lg = 2
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Tuning a FF Controller Make initial estimates of lead/lag parameters based
on process knowledge.
Under open loop conditions, adjust Kffuntil steady-
state deviation from setpoint is minimized.
Time
y
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Tuning a FF Controller
Analyzing the dynamic mismatch, adjust
ff.
Time
y
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Tuning a FF Controller
Finally, adjust (
ld -
lg) until approximately equalareas above and below the setpoint result.
Time
y
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Demonstration: Visual BasicSimulator
Tuning a FF Controller
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Feedback Control
Can effectively eliminate disturbances forfast responding processes.
But it waits until the disturbance upsets the
process before taking corrective action.
Can become unstable due to nonlinearity
and disturbance upsets.
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Feedforward Control
Compensates for ds before process is affected
Most effective for slow processes and for
processes with significant deadtime.
Can improve reliability of the feedbackcontroller by reducing the deviation from
setpoint.
Since it is a linear controller, its performance
will deteriorate with nonlinearity.
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Combined FF and FB Control
Cfb
(s)Ysp(s)
Gp(s)
Y(s)++
++
+-G
c(s)
D(s)
Gd(s)
Gff(s)
Cff(s)
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Combined FF and FB for the
CSTR
Steam
Feed
Product
TT
FT
FC
+
TC
TT
FF
RSP
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Results for CSTR
-6
-3
0
3
6
0 10 20 30 40 50Time (seconds)
T'(K)
FB-only
FF+FBFF-only
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Analysis of Results for CSTR
FB-only returns to setpoint quickly but haslarge deviation from setpoint.
FF-only reduces the deviation from setpointbut is slow to return to setpoint.
FF+FB reduces deviation from setpoint and
provides fast return to setpoint.
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Example
TTPT
Condensate
Steam
Feed
TT
Draw schematic: For a combined feedforward and
feedback controller in which the inlet feed temperatureis the feedforward variable and the outlet temperature
is the feedback variable. The combined controller
output is the setpoint for a steam pressure controller.
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Solution
TT PT
PCTC
Condensate
Steam
RSP
Feed
TT
FF
+
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Overview Cascade can effectively remove certain
disturbances if the slave loop is at least 3times faster than the master loop.
Ratio control is effective for processes that
scale with the feed rate. Feedforward can be effective for measured
disturbances for slow responding processes
as long as the process nonlinearity is not too
great.
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